Symplecticity-preserving continuous-stage Runge–Kutta–Nyström methods

Wensheng Tang and Jingjing Zhang

Applied Mathematics and Computation, 2018, vol. 323, issue C, 204-219

Abstract: In this paper, we develop continuous-stage Runge–Kutta–Nyström (csRKN) methods for numerical integration of second-order ordinary differential equations (ODEs) written in the form q¨=f(t,q). Numerous ODEs in such form can be reduced to first-order ODEs with the separable form of Hamiltonian systems and symplecticity-preserving discretizations of these systems are of interest. For the sake of designing symplectic csRKN methods, we explore the sufficient conditions for symplecticity, and we show a simple way to derive symplectic RKN-type integrators by using Legendre polynomial expansion. Numerical results show the efficiency of the presented methods.

Keywords: Hamiltonian systems; Symplecticity-preserving; Continuous-stage Runge–Kutta–Nyström methods; Legendre polynomial; Symplectic conditions (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:323:y:2018:i:c:p:204-219

DOI: 10.1016/j.amc.2017.11.054

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